This project seeks to estimate sport fish harvest and releases of rockfish in Alaska waters by improving on the Howard et al. (2020) methods and expand the time series back to 1977 when the statewide harvest survey (SWHS) was first implemented. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and replaces the Howard decision tree approach to low sample sizes with a hierarchical model. The methods and results for generating harvest estimates are generally consistent between the Bayesian model and the Howard methods. Harvest estimates are consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data.

The Bayesian methods depart from the Howard method in how releases are estimated. The Howard methods assume that the species composition of the harvests are equal to the species composition of released fish, which is clearly contraindicated in the logbook data. For instance, logbook data demonstrates that yelloweye have been retained at high levels up until restrictions were enacted in recent years, whereas pelagic rockfish were released in significant numbers in the past with retention increasing in recent years as they have become more prized by anglers. Recent prohibition on retaining yelloweye in Southeast Alaska highlights the shortcomings of the original Howard assumptions as the species composition of the harvest would indicate that no yelloweye were caught and released during the closure.

The Howard method for estimating releases for private anglers also relied on an expansion of the logbook release estimates based on the ratio of private:guided releases of all rockfish in the SWHS. In addition to the faulty assumptions about species composition, this method ignores potential bias in SWHS estimates of harvests and releases or at least assumes that the bias in release and harvests are the same. As demonstrated in Figure 1, the bias in those two quantities appears to be quite different based on the logbook data. The Bayesian model thus attempts to estimate release probabilities based on the logbook data coupled with bias corrected estimates from the SWHS.

Lastly, the Howard methods were only used on data beginning in 1999 with the advent of the logbook program and estimates of harvests and releases prior to that have been based on linear ramps from 1999 back to the perceived start of the fishery. The Bayesian methods allow us to expand the time series back to 1977 when the SWHS was implemented by leveraging regional data trends in species composition and the proportion of caught rockfish harvested by species and/or species complex. Key advantages of the Bayesian approach are highlighted in table 1.

Table 1. Summary of key improvements in reconstructiing sport fish removals of rockfish using the Bayesian model as compared to the Howard et al. (2020) methods.
Issue Howard Bayes
Time series 1999 - present 1977 - present
Bias in SWHS Not explicitly dealt with. Relies on logbook data and ratios of guided/unguided from SWHS data to estimate unguided releases and harvests. Explicitly estimates bias in SWHS harvest and release estimates based on logbook data.
Species composition of releases Assumes that species composition of releases is equal to that of the harvest, which is not evident in the logbook data. Recognizes different release probabilities by species / species assemblage and estimates it from logbook data and bias corrected SWHS data
Sample size limitations Uses sample size threshholds such that when areas fall below those threshholds values are borrowed from nearby areas. Uses a hierarchichacal modelling approach that shares information between areas in the same region. Thus all data is used, even with small sample sizes. This is a more sound method that avoids assumptions and uses all of the data.
Error propogation Error is propogated when variance estimates are available, but there is uncertainty associated with borrowing values from nearby areas, or the assumption of species compositions being identical in harvest and releases, are not dealt with. By breaking the assumption that species composition is equal between harvests and releases, uncertainty in the release estimates is more reflective of the fishery. Furthermore, the hyerarchichal approach more accurately captures uncertainy within and between areas within a region.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are overall harvest estimates from 1977- 1995 and release estimates from 1990-1995 that required some partitioning to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied to the pre-1996 values.

**Figure 1.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units. Note that initial rockfish harvest estimates were not differentiated into species assemblage or species until 1998 when logbooks began differentiating by pelagic and non-pelagic. Logbooks began to collect data on yelloweye beginning in 2006. Port sampling programs to gather data on species composition of harvests began in 1996 in Southcentral and Kodiak and in 2006 in Southeast.

Figure 1.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units. Note that initial rockfish harvest estimates were not differentiated into species assemblage or species until 1998 when logbooks began differentiating by pelagic and non-pelagic. Logbooks began to collect data on yelloweye beginning in 2006. Port sampling programs to gather data on species composition of harvests began in 1996 in Southcentral and Kodiak and in 2006 in Southeast.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook records are a census of guided harvests and releases.

SWHS Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides have been required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 2.**- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).

Figure 2.- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).


A note on model development

To evaluate the discrepancy in apparent bias in harvest and release data, several models were explored to estimate releases during model development. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treated the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases. This tensions eventually highlighted the different release/retention probabilities between yelloweye and pelagics in the logbook data and prompted the current approach whereby that probability was calculated for the three main species complexes covered in the data: pelagics, yelloweye, and “other”. The methods described here follow the (\(LB_{fit}\)) formulation. Based on model behavior it is unlikely that the (\(LB_{cens}\)) model would work as there would not be enough data to estimate release probabilities. However, it may be worth running the (\(LB_{hyb}\)) approach as a sensitivity test at the very least.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish. In Southeast Alaska, the number of Demersal Shelf Rockfish (DSR, of which yelloweye are one species) and slope rockfish are also recorded.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta0_{(comp)ayu} + \frac{\beta1_{(comp)ayu}}{(1 + exp(\beta2_{(comp)ayu}*(y - \beta3_{(comp)ayu})))} + \beta4_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior. \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernible change in composition over the observed time period. \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was used for hindcasting.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested, \(pH_{(comp)ayu}\), by area, year, user group and species grouping. Because release data from the SWHS is for all rockfish and the release data from logbooks is only subdivided into pelagics, yelloweye and “other” (non-pelagic, non-yelloweye), we only estimated \(pH_{(comp)ayu}\) for those categories. Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases. For non-yelloweye DSR and Slope rockfish assemblages in Southeast Alaska \(R_{(DSR)ayu}\) and \(R_{(slope)ayu}\) were estimated from \(R_{(other)ayu}\) using the species composition data from the harvest, thus assuming that slope and DSR assemblages were caught and released at the same rates.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta0_{(pH)ayu} + \frac{\beta1_{(pH)ayuc}}{(1 + exp(\beta2_{(pH)ayuc}*(y - \beta3_{(pH)ayuc})))} + \beta4_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990. As with the compositional trends, \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernable change in harvest probability over the observed time period, \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was applied.

Release mortality (i.e., the number of released rockfish expected to die) was calculated assuming fixed mortality rates developed in each of the regions. Deep water release (DWR) devices were mandated for charter fleets in 2013 and rates were derived from CITATION. Southeast applies basic rates estimated in these studies while Southcentral and Kodiak rates were derived by using historical depth-of-release data to adjust the rates based on area and user group.

The total number of mortalities by year, area, user and species/species assemblage in numbers was calculated by summing harvests and release mortality such that

\[\begin{equation} M_{(comp)ayu}~=~ H_{(comp)ayu} + m_{R-(comp)ayu} * R_{(comp)ayu} \end{equation}\]

where \(m_{R-(comp)ayu}\) is the release mortality rate by year, area, user and species (Figure XX).

Total removals in biomass were converted using the average weight of fish from port sampling?. A minimum sample size per year of X fish was used as the cutoff for including in the data set. Weights were modeled hierarchically to estimate weights in years when data was missing. The total biomass of removals by year, area, user and species was thus

\[\begin{equation} B_{(comp)ayu}~=~ \overline{wt}_{(comp)ayu} * M_{(comp)ayu} \end{equation}\]

where \(\overline{wt}_{(comp)ayu}\) is the mean weight by species, area, user and year.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. As such, the release data are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), a second approaches was considered that loosened the assumption that logbook releases were a census. Methods explored to develope \(LB_{hyb}\) and \(LB_{cens}\) models are detailed at the end of this section.

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs was thus a proportion of the pelagic harvests

\[\begin{equation} x_{(black)ayu}~\sim~\textrm{Binomial}(P_{(black)ayu}, N_{ayu}^{pel}) \end{equation}\]

Yelloweye rockfish in Southcentral and Kodiak were modeled similarly as a proportion of the total number of non-pelagics such that

\[\begin{equation} x_{(yellow_{R2})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R2})ayu}, N_{ayu}^{nonpel}) \end{equation}\]

Southeast areas have several other non-pelagic groupings such that DSR and slope rockfish are a proportion of non-pelagics

\[\begin{equation} x_{(DSR)ayu}~\sim~\textrm{Binomial}(P_{(DSR)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

and

\[\begin{equation} x_{(slope)ayu}~\sim~\textrm{Binomial}(P_{(slope)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

with yelloweye in southeast a proportion of the DSR harvest

\[\begin{equation} x_{(yellow_{R1})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R1})ayu}, N_{ayu}^{DSR}). \end{equation}\].

Kodiak has limited port sampling beyond the main harbors but has a robust hydroacoustic survey that is used to quantify black rockfish abundance across the management area and uses stereocameras to derive species compositions of the hydroacoustic data. This data was used as supplementary data to further inform the model to the proportion of pelagic rockfish that are black in Kodiak areas. Angler landings in Kodiak show a higher proportion of black rockfish relative to the hydroacoustic survey and thus the proportion of black rockfish in the hydroacoustic sample related to the true proportion such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ P_{(black|pelagic)ayu} + ae_{au} \end{equation}\].

where \(ae_{au}\) is the angler effect for each area and user group modeled hierarchically around a mean of 0. Predicted \(P_{(black|pelagic)ayu}^{HA}\) assumed a beta distribution such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ beta(\alpha_{HA},\beta_{HA}) \end{equation}\]

where

\[\begin{equation} \alpha_{HA} ~=~ (P_{(black|pelagic)ayu}^{HA})^2 * \frac{1 - P_{(black|pelagic)ayu}^{HA}}{\frac{var_{P_{HA}}-1}{P_{(black|pelagic)ayu}^{HA}}}, \end{equation}\]

\[\begin{equation} \beta_{HA} ~=~ (\alpha_{HA}) * \frac{1}{P_{(black|pelagic)ayu}^{HA} - 1}, \end{equation}\]

\[\begin{equation} var_{P_{HA}} ~=~ (P_{(black|pelagic)ayu}^{HA} * cvP_{(black|pelagic)ayu}^{HA})^2 \end{equation}\]

where \(cvP_{(black|pelagic)ayu}^{HA}\) is the coefficient of variation for the hydroacoustic proportions

\[\begin{equation} cvP_{(black|pelagic)ayu}^{HA} ~=~ \frac{\sqrt{varP_{(black|pelagic)ayu}^{HA}}}{P_{(black|pelagic)ayu}^{HA}} \end{equation}\]

and the variance is approximated using the XXXX method as

\[\begin{equation} varP_{(black|pelagic)ayu}^{HA} ~=~ (\frac{1}{n_{pel}})^2 * varN_{black} + (\frac{n_{black}}{n_{pel}^2}) * varN_{pel} \end{equation}\]

where \(varN_{black}\) and \(varN_{black}\) are the variance of the estimated number of black and pelagic rockfish in the hydroacoustic survey, respectively (CITATION).

The average weight of rockfish by species, user, area and year was modeled hierarchically at several levels within regions such that

\[\begin{equation} wt_{(comp)ayu} ~\sim~ Normal(wt_{(comp)au},\sigma_{wt_{(comp)au}}) ~\sim~ Normal(wt_{(comp)a},\sigma_{wt_{(comp)a}}) ~\sim~ Normal(wt_{(comp)region},\sigma_{wt_{(comp)region}}) \end{equation}\]

where region refers to Kodiak, Southcentral and Southeast. Mean weights and variance were calculated as XXX.

Alternative likelihoods for release estimates

To loosen the assumption that logbook release data are an effective census of true releases I explored models that treated logbook release estimates as a lower bound on the estimate of true releases. In a hybrid approach yelloweye and non-pelagic releases are regarded as a reliable census (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates (where censoring implies NA values) such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

This model formulation failed such that there was not enough data to inform pelagic releases and the values did not seem valid. A second approach is being explored that fits the censored data using a lognormal distribution centered around the logbook release value, but also with a lower bound equal to the number of recorded releases such that

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Logbook data is assumed to be a census and as such there is no estimate of uncertainty. As of this writing, several methods are being examined for how to treat \(\sigma_{Ray1}^2\). Models are being run that attempt to allow the model to estimate \(\sigma_{Ray1}^2\) with priors. A simple model applies a uniform prior (0.1,50) to \(\sigma_{Ray1}^2\). A hierarchichal approach based on regions is also being examined whereby \(\sigma_{Ray1}^2\) is lognormally distributed around hyper priors \(\mu_{\sigma_R}\) and \(\sigma_{\sigma_R}\). Initial efforts have applied a uniform prior on \(\mu_{\sigma_R}\) between 1 and 50 and on \(\sigma_{\sigma_R}\) between 0 and 10.

Priors.

Priors range from uninformative to very informative or fixed. Priors for compositional logistic parameters are in Table 2 and proportion harvest logistic parameters are in Table 3. Until I figure out how to make a nice table in Rmarkdown, please refer to the attached spreadsheet and comp and harvp tabs.

Unresolved issues and outstanding questions:

  1. Reliability of unguided release estimates: These estimates have the least information feeding them and rely on the bias-corrected SWHS release estimates of all rockfish and the trends in release probability evident in the logbook data. The \(\beta4\) term that estimates the guided/unguided effect was given a very informative prior that tied the release probability of private anglers tightly to that of the charter fleet. The model is then trying to balance the three species complex estimates (pelagic, yelloweye and other) so that they sum to the total unguided releases estimated from the bias corrected SWHS data. For the most part this seems reasonable and appears to work, but there are certain areas where the estimates are “wonky”:

    1. Total rockfish releases more or less align with the total releases estimated with the Howard methods. Presumably, much of the discrepancy results from the substantial bias in release estimates from the SWHS. Interestingly, the logbook data indicates that the SWHS underestimates harvests but overestimates releases by a significant factor (Figure 23 and 24 below).
    2. In general, release estimates of black rockfish are substantially lower than those calculated using the Howard methods. Presumably, much of this derives from the bias correction of the SWHS release estimates.
    3. Yelloweye release estimates also differ considerably from the Howard estimates, but unlike black rockfish are sometimes lower and sometimes higher. Two areas in particular are a little head scratching. Yelloweye releases in the Kodiak Northeast area in particular are significantly lower than for guided anglers with the same pattern evident in Cook Inlet to a lesser extent. Cook Inlet yelloweye numbers are very small, so this is a sample size issue with little consequence. The cause of the Kodiak northeast estimates is not clear to me at this point, but the model estimates the proportion harvested by unguided anglers to be much lower than that of guided anglers, even with the informative prior on \(\beta4\). This must be a product of the bias corrected SWHS release estimates and how the model is partitioning that estimate into the 3 species complexes, but itis a bit a of head scratcher.

  2. Proportion guided estimates: There is not much data on this proportion prior to 2011 and it is not modeled with any sort of trend as was done for species composition and harvest proportions. With the exception of Cook Inlet and North Gulf Coast areas, there is little, if any, trend apparent in the data and perhaps this approach is the best available given the data available. However, if there are data sources somewhere that could inform this part of the model they could be incorporated.

  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.

  4. Proportion harvest estimates for non-pelagic, non-yelloweye in Kodiak WKMA: I need to adjust the prior on the inflection point, \(\beta3\), so that it is forced to occur after 2006. Right now the model is estimating inflection in two Kodiak areas before that point where there is no data to justify a shift. The current inflection is a result of the hierachichal model.

  5. Proportion pelagic in PWS and CSEO: The parameters for these particular proportions are very slow to converge. For the CSEO, the estimates of the \(\beta\) parameters are similar to the other Southeast areas, but the mixing is poor over the length of the chains. In this case I think they will ultimately converge with a very long model run and the shape of the curve in the model output looks acceptable. For the two PWS areas the model seems to struggle with the disparate proportional data from the logbook and the port sampling. There is some wandering in the chains of the \(\beta0\) and \(\beta1\) terms and spikiness in the \(\beta2\) terms. I’ve been working on constraining the hyperpriors for PWS \(beta2\). Similar to CSEO, it may just entail a very long model run to reach convergence, but the shape of the curves looks reasonable.

Next steps:

Once the model is finalized, harvest and release numbers need to be converted into biomass removals. This is a two step process where release mortality estimates are applied to the release estimates to estimate the number of released rockfish that do not survive. This is based on studies and will reflect the values that the department has been using with the Howard methods. Region 2 (both Southcentral and Kodiak) have release-at-depth estimates from a number of years that they apply across all years and then calculate mortality rates based on those estiates. Southease does not have release-at-depth data and simply applies an assumed rate based on research.

Once release mortality is calculated average weight data is applied to convert numbers to biomass. The plan is to incorporate all of this into the model to propogate uncertainty into the posteriors. However, the model already takes a long time to run and I may explore a simpler approach using the posteriors from the numbers model to speed up processing.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 3.**- Total rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.





**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.





**Figure 8.**- DSR rockfish (excluding yelloweye) harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 8.- DSR rockfish (excluding yelloweye) harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 9.**- DSR rockfish releases (including yelloweye) 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 9.- DSR rockfish releases (including yelloweye) 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 11.**- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 11.- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 12.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 12.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Total Biomass Removal Estimates

**Figure 13.**- Black rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 13.- Black rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.



**Figure 14.**- Yellow rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 14.- Yellow rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

**Figure 15.**- Pelagic rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 15.- Pelagic rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


**Figure 16.**- Non-yelloweye, demersal shelf rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 16.- Non-yelloweye, demersal shelf rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


**Figure 17.**- Slope rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 17.- Slope rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


Model fit

Logbook residuals

**Figure 18.**- Residuals from logbook harvests.

Figure 18.- Residuals from logbook harvests.


SWHS residuals

**Figure 19.**- Residuals from SWHS harvests.

Figure 19.- Residuals from SWHS harvests.



**Figure 20.**- Residual of SWHS releases.

Figure 20.- Residual of SWHS releases.

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 21.**- Mean percent of harvest by charter anglers.

Figure 21.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although the model smooths out the changes and we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 22.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 22.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 23.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 23.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 24.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 24.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 25.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 25.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species. 


## NULL


## NULL

SWHS bias

Figure 23 shows the mean estimate for SWHS bias in harvests and releases. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias. Bias in release estimates is substantial and whereas the SWHS appears to underestimate harvests, it appears to greatly overestimates releases by a factor of 2 or more in most areas as derived from logbook reported releases.

**Figure 28.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 28.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS harvest bias track observations fairly well when he have guided harvest estimates. The estimates of release bias in the SWHS data track observed patterns to an extent, but appear to smooth these more volatile disagreements with the logbook data. Adam postulated in his initial start on this that some of this could be the result of the estimates of the proportion guided. This value was not modelled with a trend and thus applies a constant estimate when hindcasting. Data on these relationships could greatly improve this model.

**Figure 29.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 29.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 25 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 30.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 30.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment. For the most part, P(black|pelagic) is relatively constant across areas, with the exception of Cook Inlet and NSEI in Southeast AK. It may be worth discussing whether the shifts in those areas is a result of improved or changing species identification rather than actual shift in the species composition of the catch.

**Figure 31.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023. Kodiak panels include data from a hydroacoustic survey and the proportion of pelagic rockfish that are black in those areas (red) and the adjusted proportions based on obseved harvests for charter (blue) and private (cyan) users.

Figure 31.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023. Kodiak panels include data from a hydroacoustic survey and the proportion of pelagic rockfish that are black in those areas (red) and the adjusted proportions based on obseved harvests for charter (blue) and private (cyan) users.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 32.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 32.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 33.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 33.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 34.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 34.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



P(slope|non-pelagic & non-yellowye) For release estimates

**Figure 35.**- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.

Figure 35.- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.



Weight Fits

**Figure 36.**- Mean weights of black rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 36.- Mean weights of black rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 37.**- Mean weights of yelloweye rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 37.- Mean weights of yelloweye rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 38.**- Mean weights of non-black, pelagic rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 38.- Mean weights of non-black, pelagic rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 39.**- Mean weights of non-yelloweye, demersal shelf rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 39.- Mean weights of non-yelloweye, demersal shelf rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 40.**- Mean weights of slope rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 40.- Mean weights of slope rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


### Summary of unconverged parameters:

##  [1] "re_yellow"      "p_yellow"       "pDSR_YE_ayu"    "pDSR_YE_ay"    
##  [5] "pDSR_YE_ayg"    "re_pH"          "beta3_pH"       "beta2_pH"      
##  [9] "beta0_pH"       "Hy_ay"          "Hdnye_ay"       "Hdnye_ayg"     
## [13] "Hy_ayu"         "Tdnye_ayg"      "p_pelagic"      "Hy_ayg"        
## [17] "pH"             "beta1_pH"       "Ro_ayu"         "Ro_ay"         
## [21] "Bdnye_ayg"      "re_pelagic"     "Tp_ay"          "Ty_ayg"        
## [25] "Hp_ay"          "By_ayu"         "Ho_ayu"         "Ry_ay_mort"    
## [29] "Ry_ay"          "Ry_ayu"         "Ry_ayu_mort"    "Hp_ayg"        
## [33] "Tb_ay"          "Hb_ay"          "Tp_ayg"         "p_dsr"         
## [37] "Hd_ayg"         "Hb_ayg"         "Bb_ay"          "Rp_ay"         
## [41] "Tdnye_ay"       "Rb_ay"          "Rb_ay_mort"     "Rb_ayu"        
## [45] "Rb_ayu_mort"    "Rp_ay_mort"     "Rp_ayu"         "Rp_ayu_mort"   
## [49] "Tb_ayg"         "Ho_ayg"         "Bdnye_ay"       "Ry_ayg"        
## [53] "Ry_ayg_mort"    "H_ayg"          "Rs_ayu"         "Rs_ayu_mort"   
## [57] "Rp_ayg"         "Rp_ayg_mort"    "Rb_ayg"         "Rb_ayg_mort"   
## [61] "R_ayg"          "By_ay"          "Ho_ay"          "Ro_ayg"        
## [65] "Hd_ay"          "Tp_ayu"         "Hp_ayu"         "Bb_ayg"        
## [69] "Bb_ayu"         "Tb_ayu"         "Hb_ayu"         "By_ayg"        
## [73] "Rs_ay_mort"     "Rs_ay"          "mu2_wt"         "Rdnye_ayu"     
## [77] "Rdnye_ayu_mort" "Ty_ayu"         "beta_H"         "Hdnye_ayu"     
## [81] "Rdnye_ayg"      "Rdnye_ayg_mort" "Tdnye_ayu"      "Bdnye_ayu"     
## [85] "Ty_ay"          "mu_beta2_pH"    "Rd_ayg"         "beta4_pH"      
## [89] "Bs_ayg"         "Bs_ay"          "Rdnye_ay"       "Rdnye_ay_mort"
Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta0_yellow 4 2.574484
beta1_yellow 5 2.349362
beta0_pelagic 3 1.945501
beta3_yellow 3 1.904306
beta1_pelagic 4 1.676096
mu_beta0_yellow 1 1.557417
beta3_pH 1 1.509209
tau_beta0_pelagic 1 1.375122
beta2_pH 3 1.299903
beta1_black 1 1.293460
parameter n badRhat_avg
beta2_pelagic 4 1.271226
beta3_black 1 1.269187
tau_beta0_yellow 1 1.257716
beta0_pH 3 1.236037
beta1_pH 5 1.197761
beta2_yellow 1 1.192190
beta3_pelagic 2 1.139836
beta_H 2 1.135769
beta0_black 1 1.125625
Table 2. Summary of unconverged major parameters by area
Parameter CI NG PWSI PWSO BSAI SOKO2SAP WKMA afognak eastside northeast CSEO EWYKT NSEI NSEO SSEI SSEO
beta_H 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0
beta_H 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0
beta0_pH 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1
beta0_pH 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 1
beta1_pH 0 0 2 1 1 0 0 0 0 0 0 0 0 1 0 0
beta1_pH 0 0 1 1 1 0 0 0 0 0 0 0 0 1 0 0
beta2_pH 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0
beta2_pH 0 1 1 0 0 0 1 0 0 0 0 0 0 0 0 0
beta3_pH 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
beta3_pH 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
beta4_pH 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
H_ayg 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0
Hb_ay 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0
Hb_ayg 0 0 3 0 3 0 0 0 0 0 0 0 0 0 0 0
Hb_ayu 0 0 7 0 0 0 0 0 0 0 0 0 0 0 0 0
Hd_ay 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0
Hd_ayg 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0
Hdnye_ay 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0
Hdnye_ayg 0 0 0 0 0 0 0 0 0 0 2 0 0 4 0 0
Hdnye_ayu 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0
Ho_ay 0 0 0 0 3 0 0 0 1 0 0 0 0 0 0 0
Ho_ayg 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
Ho_ayu 0 0 0 0 3 0 0 0 17 0 0 0 0 0 0 0
Hp_ay 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0
Hp_ayg 0 0 3 0 3 0 0 0 0 0 0 0 0 0 0 0
Hp_ayu 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0
Hy_ay 0 0 0 0 2 0 0 0 0 0 2 0 0 2 0 0
Hy_ayg 0 0 0 0 4 0 0 0 0 0 1 0 0 2 0 0
Hy_ayu 0 0 0 0 2 0 0 0 0 0 2 0 0 2 0 0
mu_beta2_pH 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
p_dsr 0 0 0 0 0 0 0 0 0 0 0 5 0 3 0 0
p_pelagic 0 0 18 32 0 0 0 0 0 0 0 0 0 0 0 0
p_yellow 0 0 0 0 0 0 0 0 0 0 4 0 0 6 0 1
pDSR_YE_ay 0 0 0 0 0 0 0 0 0 0 2 0 0 4 0 1
pDSR_YE_ayg 0 0 0 0 0 0 0 0 0 0 2 0 0 3 0 1
pDSR_YE_ayu 0 0 0 0 0 0 0 0 0 0 2 0 0 3 0 0
pH 0 0 31 0 0 0 0 0 0 0 1 0 3 2 0 0
R_ayg 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0
Rb_ay 0 0 24 0 0 0 0 0 0 0 0 0 0 0 0 0
Rb_ay_mort 0 0 21 0 0 0 0 0 0 0 0 0 0 0 0 0
Rb_ayg 0 0 5 0 3 0 0 0 0 0 0 0 0 0 0 0
Rb_ayg_mort 0 0 5 0 3 0 0 0 0 0 0 0 0 0 0 0
Rb_ayu 0 0 14 1 0 0 0 0 0 0 0 0 0 0 0 0
Rb_ayu_mort 0 0 14 1 0 0 0 0 0 0 0 0 0 0 0 0
Rd_ayg 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Rdnye_ay 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Rdnye_ay_mort 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Rdnye_ayg 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Rdnye_ayg_mort 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Rdnye_ayu 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
Rdnye_ayu_mort 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
re_pelagic 0 0 9 3 0 0 0 0 0 0 5 0 0 0 0 0
re_pH 0 0 22 0 0 0 0 0 0 0 0 0 0 0 0 0
Ro_ay 0 0 0 2 14 7 1 0 0 0 0 0 0 0 0 1
Ro_ayg 0 0 0 1 1 1 0 0 0 0 0 0 0 0 0 1
Ro_ayu 0 0 0 2 14 9 1 0 1 0 0 1 0 0 0 0
Rp_ay 0 0 24 0 0 0 0 0 0 0 0 0 0 0 0 0
Rp_ay_mort 0 0 20 0 0 0 0 0 0 0 0 0 0 0 0 0
Rp_ayg 0 0 6 0 3 0 0 0 0 0 0 0 0 0 0 0
Rp_ayg_mort 0 0 6 0 3 0 0 0 0 0 0 0 0 0 0 0
Rp_ayu 0 0 15 1 0 0 1 0 0 0 0 0 0 0 0 0
Rp_ayu_mort 0 0 15 1 0 0 1 0 0 0 0 0 0 0 0 0
Rs_ay 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Rs_ay_mort 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
Rs_ayu 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 1
Rs_ayu_mort 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 1
Ry_ay 0 0 0 0 8 4 1 0 2 0 0 0 0 0 1 0
Ry_ay_mort 0 0 0 0 8 4 1 0 2 0 0 0 0 0 1 0
Ry_ayg 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0
Ry_ayg_mort 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0
Ry_ayu 0 0 0 1 9 5 1 0 1 0 0 0 0 0 1 0
Ry_ayu_mort 0 0 0 1 9 5 1 0 1 0 0 0 0 0 1 0
Tp_ay 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0
Tp_ayg 0 0 3 0 3 0 0 0 0 0 0 0 0 0 0 0
Tp_ayu 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0
beta0_black 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
beta0_pelagic 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 0
beta0_yellow 0 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1
beta1_black 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
beta1_pelagic 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0
beta1_yellow 1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 1
beta2_pelagic 0 0 1 1 0 0 0 0 0 0 1 0 1 0 0 0
beta2_yellow 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
beta3_black 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
beta3_pelagic 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0
beta3_yellow 0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 1
mu_beta0_yellow 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_pelagic 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_yellow 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.121 0.075 -0.255 -0.123 0.038
mu_bc_H[2] -0.095 0.046 -0.173 -0.099 0.008
mu_bc_H[3] -0.440 0.074 -0.577 -0.443 -0.292
mu_bc_H[4] -0.986 0.192 -1.368 -0.984 -0.616
mu_bc_H[5] 0.881 0.962 -0.157 0.702 3.043
mu_bc_H[6] -2.154 0.326 -2.798 -2.150 -1.524
mu_bc_H[7] -0.455 0.109 -0.679 -0.449 -0.248
mu_bc_H[8] 0.253 0.362 -0.337 0.221 1.054
mu_bc_H[9] -0.297 0.135 -0.567 -0.300 -0.030
mu_bc_H[10] -0.103 0.070 -0.232 -0.105 0.034
mu_bc_H[11] -0.126 0.037 -0.196 -0.126 -0.055
mu_bc_H[12] -0.256 0.105 -0.469 -0.255 -0.065
mu_bc_H[13] -0.136 0.080 -0.291 -0.138 0.019
mu_bc_H[14] -0.303 0.098 -0.504 -0.301 -0.117
mu_bc_H[15] -0.340 0.049 -0.435 -0.341 -0.243
mu_bc_H[16] -0.309 0.365 -0.943 -0.337 0.535
mu_bc_R[1] 1.318 0.140 1.043 1.317 1.599
mu_bc_R[2] 1.452 0.093 1.269 1.453 1.636
mu_bc_R[3] 1.399 0.145 1.109 1.399 1.685
mu_bc_R[4] 0.913 0.202 0.471 0.925 1.282
mu_bc_R[5] 1.204 0.459 0.313 1.199 2.095
mu_bc_R[6] -1.600 0.411 -2.410 -1.603 -0.813
mu_bc_R[7] 0.451 0.206 0.032 0.460 0.836
mu_bc_R[8] 0.539 0.189 0.164 0.540 0.900
mu_bc_R[9] 0.335 0.204 -0.081 0.345 0.696
mu_bc_R[10] 1.311 0.174 0.946 1.322 1.626
mu_bc_R[11] 1.044 0.098 0.852 1.043 1.236
mu_bc_R[12] 0.813 0.202 0.418 0.814 1.195
mu_bc_R[13] 1.028 0.106 0.821 1.028 1.239
mu_bc_R[14] 0.898 0.142 0.601 0.901 1.174
mu_bc_R[15] 0.782 0.111 0.565 0.782 0.995
mu_bc_R[16] 1.096 0.130 0.839 1.100 1.344
tau_pH[1] 4.932 0.603 3.590 5.011 5.951
tau_pH[2] 1.972 0.221 1.557 1.959 2.439
tau_pH[3] 2.155 0.215 1.749 2.148 2.600
beta0_pH[1,1] 0.570 0.177 0.212 0.572 0.911
beta0_pH[2,1] 1.378 0.194 0.971 1.383 1.744
beta0_pH[3,1] 1.569 0.426 0.909 1.475 2.590
beta0_pH[4,1] 1.583 0.235 1.067 1.601 1.996
beta0_pH[5,1] -0.850 0.292 -1.489 -0.836 -0.314
beta0_pH[6,1] -0.758 0.475 -1.920 -0.658 -0.087
beta0_pH[7,1] -0.592 0.527 -1.755 -0.579 0.451
beta0_pH[8,1] -0.662 0.286 -1.352 -0.624 -0.221
beta0_pH[9,1] -0.621 0.281 -1.249 -0.606 -0.108
beta0_pH[10,1] 0.327 0.237 -0.198 0.352 0.725
beta0_pH[11,1] -0.091 0.185 -0.407 -0.100 0.282
beta0_pH[12,1] 0.469 0.195 0.081 0.466 0.852
beta0_pH[13,1] 0.034 0.148 -0.239 0.033 0.310
beta0_pH[14,1] -0.299 0.175 -0.647 -0.299 0.024
beta0_pH[15,1] -0.035 0.197 -0.452 -0.031 0.341
beta0_pH[16,1] -0.414 0.335 -1.152 -0.368 0.097
beta0_pH[1,2] 2.827 0.160 2.489 2.834 3.127
beta0_pH[2,2] 2.886 0.135 2.613 2.887 3.149
beta0_pH[3,2] 3.129 0.153 2.844 3.124 3.448
beta0_pH[4,2] 2.948 0.130 2.694 2.947 3.200
beta0_pH[5,2] 4.739 1.313 2.951 4.489 8.017
beta0_pH[6,2] 3.119 0.207 2.718 3.116 3.532
beta0_pH[7,2] 1.830 0.192 1.448 1.833 2.209
beta0_pH[8,2] 2.876 0.180 2.512 2.881 3.227
beta0_pH[9,2] 3.441 0.219 3.015 3.439 3.869
beta0_pH[10,2] 3.679 0.206 3.277 3.677 4.092
beta0_pH[11,2] -4.837 0.317 -5.505 -4.809 -4.250
beta0_pH[12,2] -4.783 0.373 -5.560 -4.768 -4.079
beta0_pH[13,2] -4.575 0.380 -5.321 -4.577 -3.825
beta0_pH[14,2] -5.486 0.487 -6.515 -5.454 -4.650
beta0_pH[15,2] -4.322 0.347 -4.945 -4.336 -3.605
beta0_pH[16,2] -4.809 0.371 -5.586 -4.795 -4.119
beta0_pH[1,3] -0.131 0.679 -1.660 -0.054 1.008
beta0_pH[2,3] 2.193 0.162 1.875 2.193 2.517
beta0_pH[3,3] 2.531 0.149 2.243 2.529 2.826
beta0_pH[4,3] 2.965 0.160 2.656 2.963 3.277
beta0_pH[5,3] 2.099 1.259 0.410 1.849 5.193
beta0_pH[6,3] 0.992 0.493 -0.183 1.026 1.873
beta0_pH[7,3] 0.636 0.174 0.305 0.636 0.983
beta0_pH[8,3] 0.312 0.188 -0.068 0.315 0.685
beta0_pH[9,3] -0.638 0.395 -1.649 -0.595 0.018
beta0_pH[10,3] 0.487 0.381 -0.443 0.534 1.113
beta0_pH[11,3] -0.172 0.324 -0.845 -0.162 0.406
beta0_pH[12,3] -0.866 0.357 -1.610 -0.839 -0.215
beta0_pH[13,3] -0.139 0.304 -0.734 -0.131 0.455
beta0_pH[14,3] -0.295 0.270 -0.824 -0.293 0.225
beta0_pH[15,3] -0.720 0.302 -1.344 -0.705 -0.167
beta0_pH[16,3] -0.413 0.300 -1.031 -0.403 0.180
beta1_pH[1,1] 3.085 0.342 2.512 3.051 3.839
beta1_pH[2,1] 2.140 0.312 1.551 2.134 2.771
beta1_pH[3,1] 1.873 0.649 0.023 1.919 2.993
beta1_pH[4,1] 2.390 0.399 1.790 2.329 3.380
beta1_pH[5,1] 2.292 0.348 1.694 2.267 3.062
beta1_pH[6,1] 3.814 1.048 2.345 3.593 6.472
beta1_pH[7,1] 2.809 1.041 0.826 2.744 5.158
beta1_pH[8,1] 3.872 0.829 2.671 3.748 5.764
beta1_pH[9,1] 2.301 0.352 1.685 2.267 3.075
beta1_pH[10,1] 2.256 0.331 1.706 2.230 3.045
beta1_pH[11,1] 3.265 0.225 2.835 3.273 3.669
beta1_pH[12,1] 2.566 0.228 2.097 2.568 3.005
beta1_pH[13,1] 2.934 0.211 2.534 2.932 3.354
beta1_pH[14,1] 3.398 0.230 2.950 3.396 3.849
beta1_pH[15,1] 2.532 0.246 2.073 2.525 3.032
beta1_pH[16,1] 3.992 0.605 3.099 3.913 5.363
beta1_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,2] 0.000 0.003 0.000 0.000 0.001
beta1_pH[4,2] 0.000 0.001 0.000 0.000 0.001
beta1_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[11,2] 6.671 0.360 6.007 6.645 7.470
beta1_pH[12,2] 6.440 0.434 5.642 6.424 7.343
beta1_pH[13,2] 6.951 0.424 6.128 6.953 7.812
beta1_pH[14,2] 7.116 0.511 6.222 7.080 8.208
beta1_pH[15,2] 6.790 0.381 6.036 6.788 7.519
beta1_pH[16,2] 7.394 0.422 6.621 7.387 8.283
beta1_pH[1,3] 4.717 1.609 2.190 4.503 8.018
beta1_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[5,3] 3.732 4.882 0.904 2.794 14.590
beta1_pH[6,3] 3.101 3.199 0.461 2.644 9.605
beta1_pH[7,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[8,3] 2.741 0.347 2.116 2.730 3.481
beta1_pH[9,3] 2.755 0.473 1.970 2.707 3.898
beta1_pH[10,3] 2.887 0.458 2.115 2.834 3.973
beta1_pH[11,3] 2.765 0.402 2.058 2.742 3.602
beta1_pH[12,3] 4.127 0.445 3.286 4.108 5.031
beta1_pH[13,3] 1.728 0.328 1.107 1.723 2.374
beta1_pH[14,3] 2.558 0.343 1.919 2.543 3.266
beta1_pH[15,3] 2.020 0.327 1.423 2.015 2.678
beta1_pH[16,3] 1.825 0.336 1.193 1.813 2.501
beta2_pH[1,1] 0.479 0.152 0.272 0.460 0.793
beta2_pH[2,1] 0.625 0.506 0.236 0.520 1.613
beta2_pH[3,1] 0.366 0.854 -2.201 0.488 1.696
beta2_pH[4,1] 0.505 0.336 0.195 0.448 1.156
beta2_pH[5,1] 1.432 1.030 0.239 1.266 3.849
beta2_pH[6,1] 0.182 0.069 0.088 0.172 0.339
beta2_pH[7,1] 0.043 0.715 0.000 0.000 0.162
beta2_pH[8,1] 0.246 0.080 0.129 0.233 0.441
beta2_pH[9,1] 0.435 0.203 0.189 0.395 0.937
beta2_pH[10,1] 0.603 0.309 0.238 0.541 1.391
beta2_pH[11,1] 0.788 0.274 0.475 0.729 1.439
beta2_pH[12,1] 1.316 0.449 0.725 1.240 2.394
beta2_pH[13,1] 0.755 0.236 0.423 0.717 1.341
beta2_pH[14,1] 0.837 0.229 0.531 0.801 1.324
beta2_pH[15,1] 0.817 0.306 0.414 0.764 1.566
beta2_pH[16,1] 0.406 0.188 0.180 0.355 0.868
beta2_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,2] -1.950 1.822 -6.765 -1.470 -0.022
beta2_pH[4,2] -1.839 1.679 -6.179 -1.410 -0.021
beta2_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[11,2] -10.043 4.823 -22.601 -8.946 -3.938
beta2_pH[12,2] -8.651 5.497 -22.180 -7.589 -1.077
beta2_pH[13,2] -8.502 5.422 -22.222 -7.395 -1.788
beta2_pH[14,2] -9.211 5.095 -22.097 -8.011 -2.805
beta2_pH[15,2] -9.787 4.835 -22.133 -8.574 -3.681
beta2_pH[16,2] -10.049 4.742 -21.812 -8.934 -4.081
beta2_pH[1,3] 0.232 0.226 0.101 0.180 0.642
beta2_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[5,3] 9.329 6.403 -0.111 8.427 23.424
beta2_pH[6,3] 9.370 6.332 0.212 8.369 23.627
beta2_pH[7,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[8,3] 10.332 5.855 1.871 9.276 24.045
beta2_pH[9,3] 9.230 6.410 0.485 8.220 24.103
beta2_pH[10,3] 8.812 6.557 0.501 7.834 23.791
beta2_pH[11,3] -2.089 1.790 -7.127 -1.611 -0.586
beta2_pH[12,3] -2.276 1.796 -6.890 -1.802 -0.917
beta2_pH[13,3] -2.712 2.188 -8.595 -2.067 -0.747
beta2_pH[14,3] -2.623 2.079 -8.398 -2.017 -0.843
beta2_pH[15,3] -2.740 2.133 -8.977 -2.109 -0.971
beta2_pH[16,3] -2.844 2.212 -8.950 -2.139 -0.835
beta3_pH[1,1] 36.072 0.881 34.455 36.037 37.944
beta3_pH[2,1] 33.622 1.206 31.517 33.550 36.244
beta3_pH[3,1] 32.174 4.686 18.581 33.484 36.471
beta3_pH[4,1] 33.917 1.316 31.542 33.839 36.668
beta3_pH[5,1] 27.748 1.187 26.444 27.472 31.355
beta3_pH[6,1] 37.973 3.151 32.043 37.869 44.616
beta3_pH[7,1] 30.821 8.131 18.514 30.268 45.087
beta3_pH[8,1] 39.583 1.858 35.824 39.546 43.443
beta3_pH[9,1] 30.806 1.671 28.121 30.684 34.486
beta3_pH[10,1] 32.909 1.069 30.802 32.922 34.944
beta3_pH[11,1] 30.295 0.517 29.397 30.262 31.434
beta3_pH[12,1] 30.136 0.397 29.351 30.144 30.890
beta3_pH[13,1] 33.198 0.605 32.111 33.171 34.426
beta3_pH[14,1] 32.031 0.478 31.118 32.013 32.993
beta3_pH[15,1] 31.171 0.666 29.842 31.165 32.476
beta3_pH[16,1] 31.984 1.079 30.246 31.830 34.632
beta3_pH[1,2] 30.046 7.887 18.494 29.038 44.985
beta3_pH[2,2] 29.873 7.978 18.419 28.835 45.075
beta3_pH[3,2] 30.122 7.956 18.444 29.311 44.880
beta3_pH[4,2] 29.977 7.942 18.477 29.221 44.724
beta3_pH[5,2] 29.755 7.858 18.378 28.936 44.842
beta3_pH[6,2] 29.815 7.953 18.562 28.858 44.928
beta3_pH[7,2] 30.083 7.895 18.503 29.311 44.678
beta3_pH[8,2] 30.023 7.869 18.433 29.199 44.936
beta3_pH[9,2] 30.016 7.954 18.392 29.339 44.819
beta3_pH[10,2] 29.818 7.948 18.406 28.723 44.715
beta3_pH[11,2] 43.410 0.182 43.115 43.396 43.785
beta3_pH[12,2] 43.189 0.201 42.946 43.135 43.745
beta3_pH[13,2] 43.874 0.142 43.496 43.915 44.039
beta3_pH[14,2] 43.294 0.205 43.046 43.234 43.809
beta3_pH[15,2] 43.421 0.198 43.111 43.397 43.830
beta3_pH[16,2] 43.490 0.192 43.146 43.490 43.847
beta3_pH[1,3] 39.286 3.266 32.848 39.146 45.369
beta3_pH[2,3] 30.350 7.917 18.561 29.782 44.958
beta3_pH[3,3] 30.177 7.861 18.450 29.387 44.779
beta3_pH[4,3] 30.397 7.989 18.497 29.649 44.895
beta3_pH[5,3] 36.663 3.855 31.241 36.088 44.965
beta3_pH[6,3] 40.425 3.516 31.699 40.762 45.636
beta3_pH[7,3] 37.813 4.274 31.350 37.473 45.373
beta3_pH[8,3] 41.502 0.263 41.065 41.493 41.947
beta3_pH[9,3] 33.461 0.602 31.514 33.551 34.289
beta3_pH[10,3] 35.855 0.802 33.424 36.037 36.875
beta3_pH[11,3] 41.828 0.761 40.270 41.862 43.182
beta3_pH[12,3] 41.723 0.395 40.942 41.743 42.468
beta3_pH[13,3] 42.702 0.869 41.086 42.679 44.654
beta3_pH[14,3] 41.130 0.585 39.949 41.143 42.215
beta3_pH[15,3] 42.513 0.652 41.216 42.558 43.730
beta3_pH[16,3] 42.936 0.722 41.292 43.035 44.178
beta0_pelagic[1] 2.224 0.135 1.961 2.221 2.491
beta0_pelagic[2] 1.519 0.129 1.252 1.523 1.758
beta0_pelagic[3] -0.732 0.820 -2.222 -0.682 0.542
beta0_pelagic[4] -0.537 0.868 -2.184 -0.308 0.729
beta0_pelagic[5] 1.190 0.252 0.647 1.197 1.658
beta0_pelagic[6] 1.465 0.267 0.881 1.487 1.944
beta0_pelagic[7] 1.612 0.219 1.192 1.605 2.068
beta0_pelagic[8] 1.767 0.206 1.382 1.764 2.209
beta0_pelagic[9] 2.471 0.316 1.856 2.479 3.039
beta0_pelagic[10] 2.497 0.210 2.048 2.504 2.884
beta0_pelagic[11] -0.314 0.423 -1.348 -0.255 0.328
beta0_pelagic[12] 1.686 0.145 1.400 1.687 1.971
beta0_pelagic[13] 0.311 0.190 -0.066 0.313 0.673
beta0_pelagic[14] -0.210 0.322 -0.997 -0.170 0.302
beta0_pelagic[15] -0.274 0.151 -0.570 -0.281 0.041
beta0_pelagic[16] 0.157 0.338 -0.596 0.225 0.633
beta1_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[3] 2.432 1.366 0.460 2.169 5.102
beta1_pelagic[4] 2.237 1.306 0.477 2.061 4.829
beta1_pelagic[5] -0.075 0.315 -0.693 -0.079 0.546
beta1_pelagic[6] -0.096 0.459 -0.869 -0.154 0.758
beta1_pelagic[7] -0.034 0.298 -0.614 -0.037 0.540
beta1_pelagic[8] -0.012 0.287 -0.585 -0.007 0.557
beta1_pelagic[9] 0.216 0.486 -0.755 0.325 0.972
beta1_pelagic[10] 0.069 0.268 -0.453 0.068 0.600
beta1_pelagic[11] 4.563 0.899 3.040 4.569 6.628
beta1_pelagic[12] 2.822 0.372 2.204 2.801 3.627
beta1_pelagic[13] 3.021 0.736 1.824 2.966 4.580
beta1_pelagic[14] 4.906 1.170 3.076 4.740 7.441
beta1_pelagic[15] 2.962 0.268 2.435 2.961 3.509
beta1_pelagic[16] 4.098 1.172 2.755 3.670 6.954
beta2_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[3] 0.617 2.174 0.029 0.112 5.294
beta2_pelagic[4] 1.103 2.799 0.024 0.254 10.022
beta2_pelagic[5] -0.002 0.655 -1.361 -0.013 1.364
beta2_pelagic[6] -0.107 0.693 -1.460 -0.158 1.323
beta2_pelagic[7] 0.011 0.648 -1.399 0.002 1.322
beta2_pelagic[8] 0.006 0.642 -1.364 0.006 1.408
beta2_pelagic[9] 0.214 0.677 -1.244 0.265 1.540
beta2_pelagic[10] 0.019 0.634 -1.410 0.034 1.340
beta2_pelagic[11] 0.197 0.066 0.096 0.188 0.364
beta2_pelagic[12] 4.678 4.158 0.647 3.436 15.819
beta2_pelagic[13] 0.859 1.678 0.203 0.445 4.426
beta2_pelagic[14] 0.274 0.104 0.131 0.255 0.533
beta2_pelagic[15] 4.950 4.182 0.999 3.684 16.034
beta2_pelagic[16] 2.649 4.277 0.180 0.571 14.974
beta3_pelagic[1] 29.803 7.872 18.484 28.639 44.872
beta3_pelagic[2] 29.705 7.761 18.495 28.542 45.125
beta3_pelagic[3] 27.865 5.910 18.727 27.414 41.854
beta3_pelagic[4] 26.248 6.295 18.507 24.842 42.898
beta3_pelagic[5] 29.905 8.221 18.461 28.197 45.096
beta3_pelagic[6] 31.994 6.583 19.280 31.930 44.320
beta3_pelagic[7] 29.814 8.127 18.367 28.669 45.081
beta3_pelagic[8] 29.883 8.058 18.408 28.768 44.945
beta3_pelagic[9] 30.934 6.215 19.182 30.941 43.181
beta3_pelagic[10] 29.744 8.238 18.441 28.180 45.181
beta3_pelagic[11] 41.830 2.750 35.064 42.448 45.722
beta3_pelagic[12] 43.489 0.354 42.953 43.460 44.248
beta3_pelagic[13] 42.941 1.203 40.542 42.928 45.304
beta3_pelagic[14] 42.955 1.649 39.730 42.997 45.791
beta3_pelagic[15] 43.085 0.307 42.399 43.117 43.618
beta3_pelagic[16] 43.039 1.050 40.699 43.124 45.525
mu_beta0_pelagic[1] 0.557 1.159 -1.943 0.631 2.856
mu_beta0_pelagic[2] 1.816 0.386 1.040 1.833 2.538
mu_beta0_pelagic[3] 0.226 0.509 -0.850 0.236 1.236
tau_beta0_pelagic[1] 0.419 0.517 0.048 0.254 1.776
tau_beta0_pelagic[2] 2.882 3.413 0.245 2.070 9.913
tau_beta0_pelagic[3] 1.299 0.983 0.157 1.063 3.761
beta0_yellow[1] -0.536 0.197 -0.999 -0.517 -0.204
beta0_yellow[2] 0.502 0.167 0.186 0.511 0.804
beta0_yellow[3] -0.307 0.166 -0.627 -0.307 0.022
beta0_yellow[4] 0.874 0.213 0.384 0.897 1.225
beta0_yellow[5] -0.293 0.354 -0.984 -0.289 0.392
beta0_yellow[6] 1.113 0.166 0.791 1.113 1.443
beta0_yellow[7] 0.988 0.156 0.688 0.989 1.295
beta0_yellow[8] 1.005 0.154 0.704 1.003 1.298
beta0_yellow[9] 0.659 0.157 0.347 0.659 0.959
beta0_yellow[10] 0.590 0.141 0.312 0.590 0.867
beta0_yellow[11] -1.304 0.948 -2.731 -1.606 0.143
beta0_yellow[12] -3.778 0.424 -4.679 -3.767 -3.001
beta0_yellow[13] -3.740 0.488 -4.800 -3.710 -2.899
beta0_yellow[14] -1.559 0.993 -3.065 -1.880 0.110
beta0_yellow[15] -2.732 0.435 -3.660 -2.695 -1.907
beta0_yellow[16] -2.258 0.532 -3.184 -2.312 -1.093
beta1_yellow[1] 1.039 2.772 0.007 0.666 4.169
beta1_yellow[2] 1.068 0.389 0.580 1.015 2.041
beta1_yellow[3] 0.692 0.236 0.217 0.695 1.123
beta1_yellow[4] 1.256 0.553 0.620 1.129 2.995
beta1_yellow[5] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[6] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[7] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[8] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[9] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[10] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[11] 1.393 1.015 0.000 1.780 2.886
beta1_yellow[12] 2.571 0.432 1.791 2.549 3.528
beta1_yellow[13] 2.871 0.490 2.042 2.835 3.984
beta1_yellow[14] 1.664 0.996 0.003 1.939 3.325
beta1_yellow[15] 1.974 0.442 1.142 1.944 2.943
beta1_yellow[16] 2.013 0.533 0.830 2.067 2.933
beta2_yellow[1] -3.557 3.121 -11.626 -2.690 -0.046
beta2_yellow[2] -3.501 3.029 -11.271 -2.570 -0.200
beta2_yellow[3] -3.216 3.018 -11.574 -2.022 -0.259
beta2_yellow[4] -3.322 3.357 -12.688 -2.222 -0.137
beta2_yellow[5] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[6] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[7] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[8] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[9] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[10] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[11] -5.229 3.636 -14.807 -4.402 -0.908
beta2_yellow[12] -5.320 2.983 -12.761 -4.695 -1.285
beta2_yellow[13] -5.054 2.808 -12.142 -4.457 -1.511
beta2_yellow[14] -5.021 3.140 -12.937 -4.473 -0.355
beta2_yellow[15] -4.868 3.085 -12.675 -4.120 -1.039
beta2_yellow[16] -5.319 3.005 -12.915 -4.716 -1.343
beta3_yellow[1] 25.822 7.209 18.231 22.766 44.073
beta3_yellow[2] 29.085 1.894 24.749 28.915 32.860
beta3_yellow[3] 32.901 2.819 26.649 32.879 38.504
beta3_yellow[4] 29.094 3.180 23.691 28.071 35.713
beta3_yellow[5] 30.069 7.992 18.446 29.054 44.996
beta3_yellow[6] 29.883 7.936 18.356 28.748 45.004
beta3_yellow[7] 29.995 7.982 18.426 29.151 45.056
beta3_yellow[8] 30.150 8.002 18.515 29.145 44.900
beta3_yellow[9] 30.044 7.896 18.574 29.120 44.886
beta3_yellow[10] 30.092 7.871 18.416 29.310 44.736
beta3_yellow[11] 43.332 3.557 33.911 45.024 45.961
beta3_yellow[12] 43.329 0.368 42.622 43.302 44.060
beta3_yellow[13] 44.864 0.396 44.011 44.947 45.536
beta3_yellow[14] 42.319 3.776 33.472 43.973 45.820
beta3_yellow[15] 45.069 0.538 44.044 45.044 45.956
beta3_yellow[16] 44.494 0.903 43.301 44.525 45.797
mu_beta0_yellow[1] 0.092 0.570 -1.075 0.095 1.247
mu_beta0_yellow[2] 0.647 0.334 -0.089 0.667 1.286
mu_beta0_yellow[3] -2.142 0.834 -3.376 -2.290 -0.153
tau_beta0_yellow[1] 1.737 2.178 0.100 1.160 6.769
tau_beta0_yellow[2] 3.453 4.237 0.277 2.329 13.402
tau_beta0_yellow[3] 1.119 2.463 0.064 0.557 5.098
beta0_black[1] -0.074 0.160 -0.383 -0.074 0.231
beta0_black[2] 1.918 0.130 1.670 1.916 2.174
beta0_black[3] 1.321 0.130 1.068 1.319 1.577
beta0_black[4] 2.433 0.134 2.166 2.435 2.701
beta0_black[5] 4.658 2.091 1.784 4.235 10.048
beta0_black[6] 4.597 1.972 2.264 4.067 9.907
beta0_black[7] 3.752 1.934 1.569 3.240 8.904
beta0_black[8] 0.956 0.210 0.545 0.954 1.378
beta0_black[9] 2.611 0.231 2.146 2.613 3.072
beta0_black[10] 1.458 0.133 1.205 1.455 1.720
beta0_black[11] 3.484 0.156 3.175 3.486 3.791
beta0_black[12] 4.866 0.173 4.541 4.861 5.220
beta0_black[13] -0.169 0.397 -1.403 -0.118 0.341
beta0_black[14] 2.853 0.159 2.543 2.854 3.169
beta0_black[15] 1.294 0.157 0.989 1.290 1.617
beta0_black[16] 4.271 0.159 3.955 4.273 4.588
beta2_black[1] 7.281 9.197 0.522 3.439 35.644
beta2_black[2] 0.000 0.000 0.000 0.000 0.000
beta2_black[3] 0.000 0.000 0.000 0.000 0.000
beta2_black[4] 0.000 0.000 0.000 0.000 0.000
beta2_black[5] 0.000 0.000 0.000 0.000 0.000
beta2_black[6] 0.000 0.000 0.000 0.000 0.000
beta2_black[7] 0.000 0.000 0.000 0.000 0.000
beta2_black[8] 0.000 0.000 0.000 0.000 0.000
beta2_black[9] 0.000 0.000 0.000 0.000 0.000
beta2_black[10] 0.000 0.000 0.000 0.000 0.000
beta2_black[11] 0.000 0.000 0.000 0.000 0.000
beta2_black[12] 0.000 0.000 0.000 0.000 0.000
beta2_black[13] -1.812 1.618 -6.524 -1.306 -0.125
beta2_black[14] 0.000 0.000 0.000 0.000 0.000
beta2_black[15] 0.000 0.000 0.000 0.000 0.000
beta2_black[16] 0.000 0.000 0.000 0.000 0.000
beta3_black[1] 41.797 1.000 39.920 41.958 43.219
beta3_black[2] 25.000 0.000 25.000 25.000 25.000
beta3_black[3] 25.000 0.000 25.000 25.000 25.000
beta3_black[4] 25.000 0.000 25.000 25.000 25.000
beta3_black[5] 25.000 0.000 25.000 25.000 25.000
beta3_black[6] 25.000 0.000 25.000 25.000 25.000
beta3_black[7] 25.000 0.000 25.000 25.000 25.000
beta3_black[8] 25.000 0.000 25.000 25.000 25.000
beta3_black[9] 25.000 0.000 25.000 25.000 25.000
beta3_black[10] 25.000 0.000 25.000 25.000 25.000
beta3_black[11] 25.000 0.000 25.000 25.000 25.000
beta3_black[12] 25.000 0.000 25.000 25.000 25.000
beta3_black[13] 38.865 2.242 34.305 39.245 40.626
beta3_black[14] 25.000 0.000 25.000 25.000 25.000
beta3_black[15] 25.000 0.000 25.000 25.000 25.000
beta3_black[16] 25.000 0.000 25.000 25.000 25.000
beta4_black[1] -0.262 0.191 -0.641 -0.262 0.104
beta4_black[2] 0.239 0.183 -0.124 0.239 0.596
beta4_black[3] -0.940 0.193 -1.313 -0.943 -0.557
beta4_black[4] 0.420 0.220 -0.016 0.421 0.861
beta4_black[5] 0.529 1.379 -1.396 0.316 3.693
beta4_black[6] 0.549 1.413 -1.345 0.326 3.739
beta4_black[7] 0.477 1.402 -1.251 0.266 3.540
beta4_black[8] -0.243 0.315 -0.871 -0.237 0.349
beta4_black[9] 0.840 0.807 -0.271 0.692 2.786
beta4_black[10] 0.054 0.187 -0.312 0.055 0.425
beta4_black[11] -0.695 0.219 -1.117 -0.701 -0.252
beta4_black[12] 0.162 0.327 -0.462 0.161 0.810
beta4_black[13] -1.182 0.220 -1.604 -1.185 -0.759
beta4_black[14] -0.184 0.244 -0.649 -0.188 0.312
beta4_black[15] -0.889 0.214 -1.341 -0.887 -0.479
beta4_black[16] -0.590 0.227 -1.045 -0.592 -0.146
mu_beta0_black[1] 1.284 0.902 -0.707 1.326 2.954
mu_beta0_black[2] 2.720 1.072 0.852 2.584 5.295
mu_beta0_black[3] 2.510 1.011 0.325 2.570 4.413
tau_beta0_black[1] 0.635 0.613 0.056 0.437 2.346
tau_beta0_black[2] 0.444 0.626 0.046 0.249 2.012
tau_beta0_black[3] 0.235 0.161 0.049 0.194 0.641
beta0_dsr[11] -2.933 0.290 -3.500 -2.937 -2.354
beta0_dsr[12] 4.564 0.286 4.002 4.560 5.133
beta0_dsr[13] -1.374 0.323 -2.023 -1.357 -0.784
beta0_dsr[14] -3.811 0.529 -4.856 -3.801 -2.859
beta0_dsr[15] -1.942 0.276 -2.468 -1.942 -1.403
beta0_dsr[16] -3.013 0.355 -3.726 -3.001 -2.346
beta1_dsr[11] 4.864 0.310 4.260 4.861 5.471
beta1_dsr[12] 6.602 10.646 2.248 5.055 18.964
beta1_dsr[13] 2.888 0.366 2.281 2.861 3.579
beta1_dsr[14] 6.474 0.554 5.443 6.465 7.578
beta1_dsr[15] 3.340 0.280 2.786 3.344 3.860
beta1_dsr[16] 5.833 0.374 5.115 5.829 6.568
beta2_dsr[11] -8.351 2.481 -14.113 -8.021 -4.612
beta2_dsr[12] -7.093 2.651 -12.801 -6.942 -2.114
beta2_dsr[13] -6.561 2.823 -12.446 -6.460 -1.414
beta2_dsr[14] -6.263 2.627 -11.820 -6.154 -1.930
beta2_dsr[15] -7.784 2.471 -13.590 -7.494 -3.763
beta2_dsr[16] -8.025 2.371 -13.658 -7.725 -4.325
beta3_dsr[11] 43.488 0.151 43.210 43.482 43.771
beta3_dsr[12] 33.941 0.769 32.051 34.116 34.814
beta3_dsr[13] 43.251 0.325 42.813 43.190 43.870
beta3_dsr[14] 43.336 0.217 43.075 43.280 43.879
beta3_dsr[15] 43.511 0.188 43.169 43.513 43.859
beta3_dsr[16] 43.438 0.159 43.167 43.429 43.760
beta4_dsr[11] 0.600 0.219 0.163 0.601 1.035
beta4_dsr[12] 0.238 0.442 -0.602 0.244 1.138
beta4_dsr[13] -0.160 0.222 -0.598 -0.157 0.273
beta4_dsr[14] 0.156 0.254 -0.357 0.162 0.646
beta4_dsr[15] 0.719 0.218 0.304 0.715 1.167
beta4_dsr[16] 0.152 0.226 -0.286 0.151 0.596
beta0_slope[11] -1.849 0.144 -2.129 -1.852 -1.555
beta0_slope[12] -4.476 0.256 -5.006 -4.468 -3.981
beta0_slope[13] -1.332 0.168 -1.673 -1.326 -1.025
beta0_slope[14] -2.676 0.165 -2.993 -2.676 -2.345
beta0_slope[15] -1.342 0.141 -1.613 -1.342 -1.059
beta0_slope[16] -2.736 0.158 -3.046 -2.735 -2.430
beta1_slope[11] 4.481 0.220 4.055 4.478 4.911
beta1_slope[12] 3.984 0.440 3.159 3.982 4.875
beta1_slope[13] 2.672 0.364 2.199 2.629 3.474
beta1_slope[14] 6.333 0.423 5.528 6.330 7.177
beta1_slope[15] 3.005 0.208 2.592 3.004 3.410
beta1_slope[16] 5.284 0.290 4.717 5.285 5.859
beta2_slope[11] 8.596 2.305 5.066 8.223 13.974
beta2_slope[12] 6.689 2.851 1.212 6.630 12.406
beta2_slope[13] 5.535 2.954 0.509 5.368 11.625
beta2_slope[14] 6.511 2.589 2.309 6.303 12.194
beta2_slope[15] 8.192 2.331 4.427 7.915 13.492
beta2_slope[16] 7.849 2.352 4.236 7.530 13.537
beta3_slope[11] 43.464 0.131 43.227 43.461 43.718
beta3_slope[12] 43.353 0.277 42.930 43.312 43.912
beta3_slope[13] 43.463 0.351 42.963 43.421 44.009
beta3_slope[14] 43.262 0.133 43.094 43.232 43.608
beta3_slope[15] 43.496 0.163 43.201 43.491 43.809
beta3_slope[16] 43.372 0.144 43.151 43.350 43.697
beta4_slope[11] -0.724 0.160 -1.043 -0.723 -0.411
beta4_slope[12] -1.155 0.461 -2.173 -1.110 -0.377
beta4_slope[13] 0.085 0.162 -0.227 0.085 0.407
beta4_slope[14] -0.094 0.193 -0.466 -0.100 0.292
beta4_slope[15] -0.760 0.158 -1.080 -0.759 -0.451
beta4_slope[16] -0.155 0.175 -0.494 -0.155 0.183
sigma_H[1] 0.202 0.056 0.100 0.198 0.323
sigma_H[2] 0.171 0.029 0.121 0.169 0.234
sigma_H[3] 0.195 0.042 0.123 0.192 0.288
sigma_H[4] 0.420 0.078 0.294 0.411 0.599
sigma_H[5] 0.998 0.216 0.606 0.986 1.478
sigma_H[6] 0.432 0.201 0.044 0.428 0.840
sigma_H[7] 0.310 0.066 0.210 0.300 0.470
sigma_H[8] 0.411 0.090 0.254 0.404 0.614
sigma_H[9] 0.524 0.123 0.333 0.507 0.800
sigma_H[10] 0.210 0.040 0.140 0.208 0.294
sigma_H[11] 0.278 0.046 0.200 0.274 0.379
sigma_H[12] 0.438 0.167 0.206 0.414 0.779
sigma_H[13] 0.215 0.037 0.153 0.212 0.294
sigma_H[14] 0.508 0.092 0.350 0.500 0.703
sigma_H[15] 0.247 0.041 0.178 0.243 0.336
sigma_H[16] 0.225 0.043 0.154 0.221 0.319
lambda_H[1] 3.129 4.246 0.153 1.756 13.982
lambda_H[2] 8.028 7.261 0.738 6.086 26.250
lambda_H[3] 6.464 9.969 0.273 3.106 33.969
lambda_H[4] 0.006 0.004 0.001 0.005 0.018
lambda_H[5] 4.021 9.197 0.037 1.096 28.239
lambda_H[6] 5.423 8.988 0.009 1.472 25.650
lambda_H[7] 0.013 0.009 0.002 0.011 0.036
lambda_H[8] 8.609 11.044 0.150 4.762 38.931
lambda_H[9] 0.015 0.010 0.003 0.013 0.042
lambda_H[10] 0.272 0.321 0.033 0.185 1.008
lambda_H[11] 0.274 0.401 0.011 0.137 1.240
lambda_H[12] 4.978 6.845 0.191 2.752 24.064
lambda_H[13] 3.489 3.297 0.226 2.610 12.410
lambda_H[14] 3.267 4.159 0.220 1.986 13.362
lambda_H[15] 0.026 0.058 0.004 0.016 0.099
lambda_H[16] 0.897 1.252 0.055 0.475 4.188
mu_lambda_H[1] 4.378 1.894 1.293 4.193 8.541
mu_lambda_H[2] 3.852 1.938 0.682 3.686 7.966
mu_lambda_H[3] 3.528 1.872 0.726 3.215 7.730
sigma_lambda_H[1] 8.684 4.292 2.038 8.027 18.386
sigma_lambda_H[2] 8.349 4.572 1.174 7.819 18.383
sigma_lambda_H[3] 6.260 3.969 0.933 5.463 16.299
beta_H[1,1] 6.915 1.095 4.202 7.100 8.505
beta_H[2,1] 9.873 0.492 8.797 9.904 10.746
beta_H[3,1] 8.003 0.787 6.101 8.096 9.276
beta_H[4,1] 9.311 7.726 -6.540 9.421 23.631
beta_H[5,1] 0.189 2.307 -4.829 0.374 4.177
beta_H[6,1] 3.284 3.798 -5.994 4.604 7.426
beta_H[7,1] 0.622 5.750 -11.503 0.971 10.823
beta_H[8,1] 1.358 3.692 -2.230 1.283 3.510
beta_H[9,1] 13.045 5.680 1.421 13.127 24.196
beta_H[10,1] 7.103 1.725 3.462 7.159 10.522
beta_H[11,1] 5.297 3.420 -2.638 6.065 9.932
beta_H[12,1] 2.634 1.059 0.795 2.540 4.941
beta_H[13,1] 9.038 0.897 7.068 9.111 10.481
beta_H[14,1] 2.176 1.017 0.065 2.161 4.213
beta_H[15,1] -6.109 3.825 -12.816 -6.378 2.110
beta_H[16,1] 3.476 2.576 -0.651 3.137 9.462
beta_H[1,2] 7.902 0.247 7.413 7.905 8.356
beta_H[2,2] 10.023 0.137 9.753 10.024 10.294
beta_H[3,2] 8.955 0.195 8.577 8.952 9.347
beta_H[4,2] 3.627 1.491 0.830 3.560 6.844
beta_H[5,2] 1.981 0.945 0.106 2.008 3.683
beta_H[6,2] 5.771 1.006 3.410 5.933 7.353
beta_H[7,2] 2.648 1.095 0.632 2.593 4.936
beta_H[8,2] 3.027 1.035 1.388 3.150 4.232
beta_H[9,2] 3.530 1.117 1.484 3.490 5.854
beta_H[10,2] 8.192 0.349 7.479 8.203 8.864
beta_H[11,2] 9.738 0.620 8.813 9.621 11.170
beta_H[12,2] 3.941 0.366 3.250 3.927 4.709
beta_H[13,2] 9.124 0.252 8.672 9.116 9.620
beta_H[14,2] 4.013 0.348 3.335 4.008 4.713
beta_H[15,2] 11.356 0.683 9.872 11.389 12.588
beta_H[16,2] 4.599 0.791 3.083 4.580 6.218
beta_H[1,3] 8.451 0.243 7.997 8.442 8.956
beta_H[2,3] 10.067 0.121 9.822 10.069 10.314
beta_H[3,3] 9.629 0.162 9.310 9.626 9.953
beta_H[4,3] -2.551 0.892 -4.355 -2.544 -0.908
beta_H[5,3] 3.864 0.610 2.622 3.883 5.023
beta_H[6,3] 7.882 1.167 6.293 7.502 10.494
beta_H[7,3] -2.800 0.664 -4.110 -2.799 -1.530
beta_H[8,3] 5.225 0.468 4.654 5.169 6.066
beta_H[9,3] -2.855 0.730 -4.326 -2.852 -1.433
beta_H[10,3] 8.687 0.281 8.127 8.688 9.252
beta_H[11,3] 8.555 0.285 7.940 8.577 9.062
beta_H[12,3] 5.254 0.322 4.481 5.294 5.777
beta_H[13,3] 8.846 0.176 8.485 8.852 9.177
beta_H[14,3] 5.720 0.278 5.111 5.742 6.195
beta_H[15,3] 10.365 0.314 9.764 10.354 11.000
beta_H[16,3] 6.333 0.583 5.098 6.383 7.321
beta_H[1,4] 8.250 0.183 7.847 8.261 8.576
beta_H[2,4] 10.125 0.121 9.866 10.135 10.334
beta_H[3,4] 10.133 0.166 9.777 10.146 10.426
beta_H[4,4] 11.801 0.463 10.863 11.816 12.680
beta_H[5,4] 5.497 0.764 4.294 5.407 7.334
beta_H[6,4] 7.055 0.917 4.942 7.332 8.297
beta_H[7,4] 8.277 0.353 7.588 8.277 8.947
beta_H[8,4] 6.712 0.240 6.260 6.718 7.144
beta_H[9,4] 7.226 0.468 6.320 7.225 8.135
beta_H[10,4] 7.722 0.227 7.293 7.715 8.176
beta_H[11,4] 9.386 0.205 8.981 9.391 9.782
beta_H[12,4] 7.143 0.218 6.724 7.138 7.615
beta_H[13,4] 9.046 0.143 8.753 9.048 9.325
beta_H[14,4] 7.735 0.219 7.313 7.733 8.163
beta_H[15,4] 9.466 0.234 9.012 9.466 9.914
beta_H[16,4] 9.343 0.238 8.927 9.329 9.836
beta_H[1,5] 8.977 0.147 8.670 8.981 9.257
beta_H[2,5] 10.784 0.093 10.605 10.781 10.978
beta_H[3,5] 10.920 0.167 10.617 10.910 11.268
beta_H[4,5] 8.377 0.468 7.478 8.362 9.323
beta_H[5,5] 5.442 0.572 4.084 5.477 6.433
beta_H[6,5] 8.817 0.644 7.926 8.649 10.429
beta_H[7,5] 6.736 0.338 6.074 6.737 7.427
beta_H[8,5] 8.210 0.205 7.857 8.201 8.600
beta_H[9,5] 8.197 0.464 7.263 8.189 9.119
beta_H[10,5] 10.103 0.218 9.679 10.109 10.524
beta_H[11,5] 11.508 0.233 11.054 11.505 11.983
beta_H[12,5] 8.486 0.196 8.111 8.483 8.889
beta_H[13,5] 10.004 0.131 9.744 10.005 10.262
beta_H[14,5] 9.200 0.233 8.768 9.190 9.682
beta_H[15,5] 11.162 0.246 10.678 11.165 11.652
beta_H[16,5] 9.930 0.175 9.576 9.939 10.271
beta_H[1,6] 10.186 0.191 9.832 10.172 10.609
beta_H[2,6] 11.511 0.109 11.292 11.511 11.719
beta_H[3,6] 10.817 0.160 10.480 10.827 11.109
beta_H[4,6] 12.900 0.821 11.235 12.906 14.536
beta_H[5,6] 5.913 0.605 4.742 5.901 7.118
beta_H[6,6] 8.836 0.677 7.043 8.966 9.814
beta_H[7,6] 9.873 0.576 8.706 9.883 10.992
beta_H[8,6] 9.512 0.266 9.008 9.527 9.966
beta_H[9,6] 8.492 0.780 7.014 8.495 10.078
beta_H[10,6] 9.503 0.313 8.850 9.524 10.059
beta_H[11,6] 10.828 0.354 10.068 10.854 11.459
beta_H[12,6] 9.379 0.256 8.920 9.365 9.901
beta_H[13,6] 11.049 0.162 10.754 11.042 11.387
beta_H[14,6] 9.824 0.288 9.223 9.827 10.394
beta_H[15,6] 10.832 0.424 10.007 10.836 11.680
beta_H[16,6] 10.552 0.241 10.045 10.567 10.989
beta_H[1,7] 10.908 0.871 8.825 11.008 12.355
beta_H[2,7] 12.217 0.431 11.334 12.220 13.051
beta_H[3,7] 10.549 0.655 9.092 10.603 11.636
beta_H[4,7] 2.348 4.151 -5.866 2.306 10.750
beta_H[5,7] 6.449 1.849 3.065 6.384 10.699
beta_H[6,7] 9.728 2.387 5.146 9.650 16.006
beta_H[7,7] 10.450 2.885 4.913 10.406 16.341
beta_H[8,7] 10.939 0.923 9.496 10.905 12.556
beta_H[9,7] 4.380 3.943 -3.587 4.507 11.925
beta_H[10,7] 9.875 1.453 7.166 9.775 13.136
beta_H[11,7] 10.965 1.693 7.881 10.864 14.567
beta_H[12,7] 9.997 0.944 7.926 10.060 11.572
beta_H[13,7] 11.639 0.761 9.846 11.744 12.791
beta_H[14,7] 10.399 0.956 8.337 10.455 12.071
beta_H[15,7] 12.013 2.247 7.625 12.027 16.465
beta_H[16,7] 12.254 1.268 10.186 12.069 15.327
beta0_H[1] 9.291 13.065 -15.940 8.987 36.150
beta0_H[2] 10.494 6.510 -3.154 10.523 23.500
beta0_H[3] 9.650 9.484 -10.356 9.842 28.376
beta0_H[4] 3.883 184.552 -369.118 0.333 380.056
beta0_H[5] 4.285 23.705 -42.770 4.384 53.514
beta0_H[6] 6.130 47.270 -105.057 7.307 111.245
beta0_H[7] 6.961 135.141 -268.609 5.766 285.921
beta0_H[8] 5.554 33.775 -17.361 6.447 28.437
beta0_H[9] 7.870 121.262 -233.288 6.398 261.236
beta0_H[10] 9.519 33.300 -57.293 9.646 74.933
beta0_H[11] 9.676 48.872 -95.843 10.231 119.378
beta0_H[12] 6.398 10.728 -16.118 6.495 30.079
beta0_H[13] 9.979 10.736 -12.200 10.113 30.779
beta0_H[14] 6.894 11.250 -15.369 6.938 28.827
beta0_H[15] 6.045 106.381 -205.813 6.490 214.522
beta0_H[16] 8.230 23.649 -38.866 7.965 60.036